论文标题
实用和结构的无限扩展
Practical and Structural Infinitary Expansions
论文作者
论文摘要
鉴于结构$ m $，我们引入了无限逻辑扩展，从而概括了伪造。我们表明，这些扩展是驯服的，从某种意义上说，它们保留并反映了嵌入Ramsey属性（ERP）和建模属性（MP）。然后，我们将注意力转移到Scow的定理上，将通用的Indiscernibles与Ramsey类连接起来，并表明，通过通过无限逻辑，可以获得更强的结果，这不需要任何技术假设。我们还表明，ERP的每个结构（不一定是可计数）都承认了一个线性顺序，该顺序是无量词类型的结合，有效地证明了任何Ramsey结构是``本质上''订购的。我们还为不一定是有限的结构类别引入了ERP版本，并证明了该概念的Kechris-Pestov-Todorcevic对应关系的加强。
Given a structure $M$ we introduce infinitary logic expansions, which generalise the Morleyisation. We show that these expansions are tame, in the sense that they preserve and reflect both the Embedding Ramsey Property (ERP) and the Modelling Property (MP). We then turn our attention to Scow's theorem connecting generalised indiscernibles with Ramsey classes and show that by passing through infinitary logic, one can obtain a stronger result, which does not require any technical assumptions. We also show that every structure with ERP, not necessarily countable, admits a linear order which is a union of quantifier-free types, effectively proving that any Ramsey structure is ``essentially'' ordered. We also introduce a version of ERP for classes of structures which are not necessarily finite (the finitary-ERP) and prove a strengthening of the Kechris-Pestov-Todorcevic correspondence for this notion.
